text: For mass numbers with more than two beta-stable isobars, quadruple beta decay and its inverse, quadruple electron capture, have been proposed as alternatives to double beta decay in the isobars with the greatest energy excess. These decays are energetically possible in eight nuclei, though partial half-lives compared to single or double beta decay are predicted to be very long; hence, quadruple beta decay is unlikely to be observed. The seven candidate nuclei for quadruple beta decay include Zr, Xe, and Nd capable of quadruple beta-minus decay, and Xe, Ba, Gd, and Dy capable of quadruple beta-plus decay or electron capture (though Gd and Dy are non-primordial alpha-emitters with geologically short half-lives). In theory, quadruple beta decay may be experimentally observable in three of these nuclei – Zr, Xe, and Nd – with the most promising candidate being Nd. Triple beta decay is also possible for Ca, Zr, and Nd.
  Moreover, such a decay mode could also be neutrinoless in physics beyond the standard model. Neutrinoless quadruple beta decay would violate lepton number in 4 units, as opposed to a lepton number breaking of two units in the case of neutrinoless double beta decay. Therefore, there is no black-box theorem and neutrinos could be Dirac particles while allowing these type of processes. In particular, if neutrinoless quadruple beta decay is found before neutrinoless double beta decay then the expectation is that neutrinos will be Dirac particles.
  So far, searches for triple and quadruple beta decay in Nd have remained unsuccessful.